Listen to Robert Emmerich introduce The Big Apple, a hit song from 1937. Music written by Bob and performed by Tommy Dorsey's Clambake Seven with Bob on piano. Lyrics written by Buddy Bernier and sung by Edythe Wright. Audio provided by Dorothy Emmerich.

The Federal Bureau of Investigation (FBI) was founded in 1908 and conducts federal criminal and intelligence investigations. The unflattering FBI nickname of “Fumbling, Bumbling Idiots” has been cited in print since at least 1975. The FBI nickname of “Fumbling, Bumbling Incompetents” has been cited in print since at least 2001.

Wikipedia: Federal Bureau of Investigation
The Federal Bureau of Investigation (FBI) is an agency of the United States Department of Justice that serves as both a federal criminal investigative body and an internal intelligence agency (counterintelligence).

It is the government agency responsible for investigating crimes on Indian Reservations in the United States under the Seven Major Crimes Act, passed in 1885. In 1953, Congress passed Public Law 280 giving state governments the right to assume civil and criminal jurisdiction over Indian reservations in California, Minnesota, Nebraska, Oregon, Wisconsin, and Alaska.

The branch has investigative jurisdiction over violations of more than 200 categories of federal crime. The agency was established in 1908 as the Bureau of Investigation (BOI). Its name was changed to the Federal Bureau of Investigation (FBI) in 1935.

The agency headquarters is the J. Edgar Hoover Building, located in Washington, D.C., along with fifty-six field offices located in major cities throughout the United States, and more than 400 resident agencies in lesser cities and areas across the nation. More than 50 international offices called “legal attachés” exist in U.S. embassies and consulates general worldwide.

14 March 1975, Dallas (TX) Morning News, “Letters from Readers,” pg. D2, col. 6:
I have never been fond of the Feebies—the Fumbling, Bumbling Idiots of the FBI.
(...)
LOUISE JAGGER.
Dallas.

27 July 1975, The Independent Record (Helena, MT), pg. 4, col. 4:
The FBI
FBI is supposed to stand for Federal Bureau of Investigation, but at times one wonders if Fumbling Bumbling Idiots wouldn’t be better.

18 September 1977, The Pioneer (Bemidji, MN), “More than doubts about the FBI” by Virginia Payette, pg. 4, col. 6:
It’s almost enough to make you wonder if FBI stands for “fumbling, bumbling inefficiency.” Say it ain’t so, Clarence.

13 June 2006, North Adams (MA) Transcript, “They deserve no love or respect‎,” Letters:
I have actually heard an MSNBC commentator say the FBI lately could be fumbling, bumbling incompetents — a little extreme.

Google BooksTiger In The Rain
By Robert Clayton Buick
Xlibris Corporation (Xlibris.com)
2010
Pg. 85:
Better described the consensus of opinions throughout local law enforcement agencies nationally are regarded as either “Fumbling Bumbling Idiots” or “Fucking Bungling Idiots.” I personally prefer the latter.

YouTubeFBI Fumbling Bumbling Idiots Once Again
Uploaded by 101Treesrus on Dec 17, 2010